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Triangle read by rows: T(n,k) = number of partitions of n that are formed by k sections, k >= 1.
1

%I #18 Feb 14 2018 09:15:48

%S 1,1,1,1,1,1,2,1,1,1,2,2,1,1,1,4,2,2,1,1,1,4,4,2,2,1,1,1,7,4,4,2,2,1,

%T 1,1,8,7,4,4,2,2,1,1,1,12,8,7,4,4,2,2,1,1,1,14,12,8,7,4,4,2,2,1,1,1,

%U 21,14,12,8,7,4,4,2,2,1,1,1,24,21,14

%N Triangle read by rows: T(n,k) = number of partitions of n that are formed by k sections, k >= 1.

%C Also triangle read by rows in which row n lists the first k terms of A187219 in reverse order. For more information see A135010.

%e Triangle begins:

%e 1,

%e 1,1,

%e 1,1,1,

%e 2,1,1,1,

%e 2,2,1,1,1,

%e 4,2,2,1,1,1,

%e 4,4,2,2,1,1,1,

%e 7,4,4,2,2,1,1,1,

%e 8,7,4,4,2,2,1,1,1,

%e 12,8,7,4,4,2,2,1,1,1,

%e 14,12,8,7,4,4,2,2,1,1,1,

%e 21,14,12,8,7,4,4,2,2,1,1,1

%Y Columns are A187219. Row sums give A000041, n >= 1.

%Y Cf. A002865, A116598, A135010, A138121, A182748, A186114, A193870, A194436-A194438, A194446.

%K nonn,tabl

%O 1,7

%A _Omar E. Pol_, Jan 30 2012